On Fermat's Last Theorem over the ${\mathbb{Z}}_3$-extension of $\mathbb{Q}$ and other fields

Luis Dieulefait, Franco Golfieri Madriaga

The main result of the present article is a proof that, over certain totally real number fields $K$, the Fermat equation $x^p+y^p+z^p=0$ has no non-trivial primitive solutions in $…